Question: Rewrite as a simplified fraction. ${0.\overline{64} = {?}}$
Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}100x &= 64.6464...\\ 1x &= 0.6464...\end{align*}}$ Subtracting the two equations, we have: ${99x = 64}$ ${x = \dfrac{64}{99}} $